Is it feasible to raise this plumbing higher? Or should I bulkhead around it?

I currently have a drop ceiling in most of my basement that is at 7' height. I want to get rid of that and go with an 8' drywall (or even high suspended) ceiling wherever possible, bulkheading around the HVAC supply/return channels. My question comes in regards to the current plumbing that is down there. At the lowest point, I would be stuck at 7' height on the ceiling to cover all this as it sits. Would it be feasible to raise it higher and tuck as much as possible between the floor joists, possibly doing just a small bulkhead against the wall or something?

Something like this, I would not handle myself; I would have a pro come in and do it. Before I waste one's time coming, I'd like to know if it's even feasible, and if so, a rough estimate (I know it varies greatly, but a ballpark) of what I'd be looking at ($500? $2500?).

Also, don't blame me for anything that is blatantly wrong or against code...I bought it this way.

Along those same lines, if it's determined that it can't be raised, or it's not worth the cost, I may just build a closet/storage room below this area. Do a drop ceiling just in that small room so that the plumbing is still accessible should I ever need to get into it.

Lastly, if anything is glaringly obvious/wrong/dangerous, feel free to point it out.

There's a limit on how many, and where you can drill holes in floor joists. Your last picture shows a distintly non-approved notching of the joist. Notches are never approved, but happen more than you'd like. That joist is now the equivalent of what's left through its full length, and now probably does not support the floor properly.

The supply lines could probably be raised, or rerouted so you could maybe have a chase at the edge of the room, but the drain lines can't go up and down, they need slope to them so gravity can do its thing. Those would be harder to reroute. It's hard to tell from pictures. Some of the drains do come down further than needed, but not sure - a pro might have a better feel for this.

When a friend had a house built, he had 10' ceilings in his basement to allow for lots of bookshelves (he's a used book dealer). At the time of construction, unless this would drop you into the water table, I'd prefer much deeper basements. Yours is typical, and unless planned for originally, basements often don't make great living spaces for full-sized people!

It COULD be done, but it would be very expensive, but we cannot tell you how expensive. All of the piping would have to be revised so it ran between the joists to the side wall where they would each connect to that, or another, horizontal pipe before continuing over and down into the main connection. In the process of repiping the drains, the "first" tub, or shower, could have a vent installed which it doesn't have now.